The pilgrims were crushed on the last day of the Hajj at the disaster-prone al-Jamarat bridge in Mina, a narrow valley near Makka, as they jostled to perform a stoning ritual in the early afternoon.
Saudi Arabia hosts about 2.5 million Hajj pilgrims from all over the world every year.
Grand Mufti Shaikh Abd al-Aziz al-Shaikh, the kingdom's most senior cleric, said on state television: "The state has made every effort and done everything it should."
He accused pilgrims of being disorderly.
Sultan bin Abdul-Aziz, the crown prince, also blamed pilgrims who defied the rules and carried their belongings with them and ignored advice to perform the ritual throughout the day.
The official Saudi Press Agency quoted Prince Nayef bin Abdul-Aziz, the interior minister, as saying: "It pains us that so many people died, but we must point out that the security forces averted many more disasters from happening and saved many lives."
Saudi Arabia's leading cleric said
the state had done its best
Khaled al-Mirghalani, a health ministry spokesman, put the toll at 362, up from 345 announced on Thursday.
He said 45 out of the 289 people initially sent to hospital, remained warded.
Husain Salih Bahashwan, deputy director at al-Muaysim mortuary, just outside Mina, said 100 Egyptians had died.
Khalid Yasin, director of evacuation operations at the health ministry, said "most of the dead are Egyptians" and that the toll included Africans, Saudis and pilgrims from several Asian countries.
India said at least 27 of its citizens were killed in the crush. Indonesia reported that two of its pilgrims had died and Pakistan said it knew of six fatalities.
Following the prophet
Many pilgrims follow the Prophet Muhammad's example of stoning after noon prayers instead of staggering the ritual throughout the day as some clerics recommend.
Saudi clerics have in the past advised stoning after noon.
But some pilgrims said the authorities had failed to impose their own rules on the ritual, at which there had been similar deadly stampedes in the past.
Jihad, a 28-year-old pilgrim from Egypt, said the high security was not very effective.
"There seemed to be more security forces this year but they were not very organised or had any plan," he said.
Yasir Bakir, 39, another Egyptian pilgrim, said security forces should have concentrated their efforts on removing squatters. "This year, they seemed to let them slide by," he said.
Witnesses also said the deaths were caused as the flow of pilgrims entering and leaving al-Jamarat bridge clashed, and people ignored instructions on huge notice boards, loudspeakers and pamphlets on how to perform the rite.
Witnesses said pilgrims ignored
instructions on the flow of traffic
Raqiya Shabib, a columnist for the Saudi-owned Al-Hayat newspaper, wrote: "'What's the reason for what happened?' that's the question that must be answered.
"For this not to happen again the organisation has got to be
rethought at the Jamarat area in particular."
The Interior Ministry said before the five-day Hajj - a duty for every Muslim who is able, at least once - that it would stop pilgrims squatting with their belongings by the side of al-Jamarat bridge.
Officials say that about 300,000 Muslims who are already resident in Saudi Arabia slip into the Makka area to join the
two million pilgrims from overseas, taking part.
This year's Hajj had already been marred by the collapse of a Makka hostel that killed 76 people last week.
In 2004, about 250 pilgrims were crushed to death at al-Jamarat bridge. A decade earlier, 270 were killed in a similar stampede.
Thursday's toll was the highest since 1426 people were killed in a stampede in a tunnel in Makka in 1990.